IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 14, 2015 1239
Radar Coincidence Imaging With Random
Microwave Source
Shitao Zhu, Anxue Zhang, Zhuo Xu, and Xiaoli Dong
Abstract—The radar coincidence imaging (RCI), as a novel
radar imaging method, is presented in this letter. Firstly, the re-
lationship between the deployment of general random microwave
array source and the resolution of RCI under second-order corre-
lation methods (SOCM) is presented. Then, the super-resolution
RCI is obtained assisted by optimization algorithms based on the
matrix form of measurement data. Finally, the mirror phenom-
enon of RCI, which is caused by the spacing of radar elements, is
presented. In experiments, we form RCI using uniform 1-D an-
tenna array with random phase and random amplitude modulated
excitation signal for each radar element. The proposed analysis is
validated through numerical simulations and experiments.
Index Terms—Ghost imaging, mirror image, radar coincidence
imaging, super-resolution.
I. INTRODUCTION
I
N THE past decade, the coincidence or ghost imaging has
increased dramatically since Pittman’s ground-breaking
work in 1995 [1]. The coincidence images are formed through
correlation between the signal from bucket detector, which has
no spatial resolution and carries the information of the target,
and the random radiation field which is detected or calculated
with high resolution and has no information of the target.
The coincidence image can be reconstructed with various il-
lumination sources, such as entangled source, thermal source,
and even multi-wavelength source [2]–[7]. For the radar coinci-
dence imaging (RCI) as shown in Fig. 1, the illumination source
is microwave radar array. The radiation fields in the test system
and in the reference system are the same, which is ensured by
the splitter in the conventional coincidence imaging [8], [9],
while the splitter is not necessary for the computational co-
incidence imaging [10], [11]. The reference filed is required
time-space-independent for the high-resolution RCI, and the
reference filed is fit to compute [12].
The resolution of the coincidence imaging is proportional
to the wavelength and is inverse proportional to the limited
Manuscript received January 12, 2015; accepted January 31, 2015. Date of
publication February 04, 2015; date of current version June 01, 2015. This
work was supported by the National Natural Science Foundation of China
under Grants 61471292, 61331005, 61471388, 51277012, and 41404095.
(Corresponding au thor: Anxue Zhang.)
S. Zhu, A. Zhang, and Z. Xu are with the School of Electronic and Infor-
mation Engineering, Xi’an Jiaotong University, Xi’an 710049, China (e-mail:
zhushitao@stu.xjtu.edu.cn; anxuezhang@mail.xjtu.edu.cn; xuzhuo@mail.xjtu.
edu.cn).
X. Dong is with the School of Telecommunication and Information Engi-
neering, Xi’an University of Posts and Telecommunications, Xi’an 710121,
China (e-mail: dxl_xaut@163.com).
Color versions of one or more of the figures in this letter are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LAWP.2015.2399977
Fig. 1. Basic architecture of RCI system.
size of the source under second-order correlation method
(SOCM) [12]–[15]. The second-order correlation function
between one point in the radiation filed with the whole radiation
field is concluded to be a somb function for light source [13]
andtobeasinc function (
function in the analysis) for the
radar source [12]. However, the relationship between the res-
olution of RCI and the deployment of the microwave source
(except the source size) under SOCM still has no generalized
conclusion. Hence, we analyze the relationship and an inter-
esting phenomenon occurs: there are mirror images in a large
imaging area when the spacing of the radar elements is bigger
than a threshold, which is similar to the array pattern of the
conventional coherent radar array [16]–[18].
In this letter, the general relationship between the resolution
of RCI and the deployment of the microwave source, as well as
the phenomenon of mirror images in RCI, are analyzed. The uni-
form 1-D antenna array is used as microwave source; the phase
and amplitude of the excitation signals are randomly modulated,
respectively, for each radar element in the experiment. Experi-
ments in a large imaging area show that, for the RCI, the high
resolution requires big radar array size, and the wide effective
imaging region, which means there is no mirror image in the
imaging region, requires small spacing between radar elements.
II. A
NALYSIS OF RCI
T
he conventional coincidence image is reproduced by cal-
culating the second-order correlation of the radiation field as
showninthefollowingequation:
(1)
where
means the ensemble average, represents position in
the target plane,
is the estimation of transmission or reflection
coefficient distribution of the target,
is the inten-
sity fluctuation of the light intensity, and
and are
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